Out of 50 people in a party,24 preferred Chinese food,18 preferred Con

Question

Out of 50 people in a party,24 preferred Chinese food,18 preferred Continental food and 20 preferred South Indian Food.What is the maximum number of people who preferred none of the three?

A. 18
B. 20
C. 24
D. 26
E. 32

johnymaung · Accepted Answer

It is D.

To find out the maximum number of people who dont like any of the three, we can utilize the venn diagram. If we need to find the maximum number of people who do not like any food, the three food categories need to overlap in such a way that they fall over each other (Refer to the diagram).

Then the maximum number of people who do not like any food will be:
Total number of people - Number of people in the largest group= 50-24=26

Ramyanag · Answer

Maximum number of people who preferred none of these foods = 50 - (Minimum number of people who preferred these three foods)
From the given data, the minimum number of people who preferred any of the three foods is 24. 
50-24=26
Answer: D

sudarshan22 · Answer

The maximum number of people who preferred none of the three foods = Total - largest number of people for a preferred food
Because, there is a chance of the other two lower number people of preferred food to be covered in the largest number of preferred food.
 i.e, 18 people who preferred Continental food and 20 people who preferred South Indian food can be overlapped with 24 people who preferred Chinese food

Therefore, 
50 - 24 = 26

Hence,   D  .

TheNightKing · Answer

Hello  sudarshan22 ,
I hope you're doing good. Can you explain this one?

I understand 18 and 20 can be overlapped with 24 but where exactly? 24 people cannot like all three. So where exactly?

Thank you!

wickedvikram · Answer

Let "x" be me max number of people uninterested in any of 3(let's call them A, B, C)

50-x = A+B+C - (AB+BC+CA) + ABC
x= 50 + (AB+BC+CA) -  
x=50 + (AB+BC+CA) -  
x= (AB+BC+CA) - (2 + ABC)

Identify Max value for (AB+BC+CA) and min value for ABC

min ABC = 0
max (AB+BC+CA) = 9 + 9 + 10 = 28
Hence x=26

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Out of 50 people in a party,24 preferred Chinese food,18 preferred Con

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